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A higher order Godunov method for the radiation subsystem of radiationhydrodynamics is presented. A key ingredient of the method is the directcoupling of stiff source term effects to the hyperbolic structure of the systemof conservation laws; it is composed of a predictor step that is based onDuhamel's principle and a corrector step that is based on Picard iteration. Themethod is second order accurate in both time and space, unsplit, asymptoticallypreserving, and uniformly well behaved from the photon free streaming(hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit andto the strong equilibrium diffusion (hyperbolic) limit. Numerical testsdemonstrate second order convergence across various parameter regimes.

A Higher Order Godunov Method for Radiation Hydrodynamics: Radiation Subsystem